Pulsed neutron capture inversions are nonlinear problems with many local minima around the absolute minimum. A Neuman pulsed neutron decay (PNC) method has been used in the past to invert PNC decay curves. This method involves fitting these decay curves produced by the tools to dual exponential response model. From the fitted parameters the sigma of both the borehole and formation can be determined. The Sigma can then be used to determine petrophysical properties such as steam saturation, water saturation or a pseudo-porosity. However, fitting these curves is not a trivial matter since the data can have poor signal to noise ratios, especially during later times (after 500 μs). It is during this time that the formation signal tends to dominate the borehole signal.
In addition to computing the Sigma values, the Neuman method also calculates PNC-based density and porosity indicators. Both of these inversions use the sigma information to produce the estimates. The Neuman code is also used to plot the PNC data and the resultant fitted curve. This allows users to visually inspect the fit. Because of the low signal to noise ratio fitting routines can often “lock on” to bad fits. Visually inspecting the curve allows users to determine if a sigma value is a statistical outlier or just a bad fit.
The Neuman method uses a Newton-Raphson method to optimize the fit the measured data to the inversion model. This method works well for problems that have a signal minimum but can run into trouble when dealing with noisy data. The method can converge to solution that are one of many local minima but is not the absolute minimum that would characterize the “best” fit. The results are that the plotted log results from this processing may contain large spikes or outliers that come from a failure to converge on the absolute minimum.
Given the problems above, what is needed is an improved method and system for inverting pulsed neutron capture decay curves.